7 citations · 9 across the 9 of their papers we have counts for
15 papers
Patrolling cop vs omniscient robber
Nina Chiarelli, Paul Dorbec, Miloš Stojaković +1
We study a variant of the classical Cops and Robbers game with one cop and one robber. The cop follows a fixed walk on the graph, called a patrol, that is chosen before the game be…
Cayley trees and increasing 1,2-trees: let's twist!
Julien Courtiel, Matthieu Dien, Paul Dorbec
An increasing 1,2-tree is a labeled graph formed by starting with a vertex and then repeatedly attaching a leaf to a vertex or a triangle to an edge, the labeling of the vertices c…
An exploration of the balance game
Paul Dorbec, Michael A. Henning, Zsolt Tuza +1
The balance game is played on a graph by two players, Admirable (A) and Impish (I), who take turns selecting unlabeled vertices of . Admirable labels the selected vertices b…
The 1/3-conjectures for domination in cubic graphs
Paul Dorbec, Michael Antony Henning
A set S of vertices in a graph G is a dominating set of G if every vertex not in S is adjacent to a vertex in S . The domination number of G, denoted by (G), is the minimum card…
Theoretical analysis of git bisect
Julien Courtiel, Paul Dorbec, Romain Lecoq
In this paper, we consider the problem of finding a regression in a version control system (VCS), such as git. The set of versions is modelled by a Directed Acyclic Graph (DAG) whe…
Orientable Burning Number of Graphs
Julien Courtiel, Paul Dorbec, Tatsuya Gima +2
In this paper, we introduce the problem of finding an orientation of a given undirected graph that maximizes the burning number of the resulting directed graph. We show that the pr…
Dominating sets reconfiguration under token sliding
Marthe Bonamy, Paul Dorbec, Paul Ouvrard
Let be a graph and and be two dominating sets of of size . Does there exist a sequence of…
Cutting Lemma and Union Lemma for the Domination Game
Paul Dorbec, Michael A. Henning, Sandi Klavžar +1
Two new techniques are introduced into the theory of the domination game. The cutting lemma bounds the game domination number of a partially dominated graph with the game dominatio…
Power domination in maximal planar graphs
Paul Dorbec, Antonio González, Claire Pennarun
Power domination in graphs emerged from the problem of monitoring an electrical system by placing as few measurement devices in the system as possible. It corresponds to a variant…
Toward Quantum Combinatorial Games
Paul Dorbec, Mehdi Mhalla
In this paper, we propose a Quantum variation of combinatorial games, generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff. A combinatorial game is a two-player game with no…
On the number of planar Eulerian orientations
Nicolas Bonichon, Mireille Bousquet-Mélou, Paul Dorbec +1
The number of planar Eulerian maps with n edges is well-known to have a simple expression. But what is the number of planar Eulerian orientations with n edges? This problem appears…
Heredity for generalized power domination
Paul Dorbec, Seethu Varghese, Ambat Vijayakumar
In this paper, we study the behaviour of the generalized power domination number of a graph by small changes on the graph, namely edge and vertex deletion and edge contraction. We…
Complexity of the Game Domination Problem
Boštjan Brešar, Paul Dorbec, Sandi Klavžar +2
The game domination number is a graph invariant that arises from a game, which is related to graph domination in a similar way as the game chromatic number is related to graph colo…
Ice sliding games
Paul Dorbec, Eric Duchêne, André Fabbri +3
This paper deals with sliding games, which are a variant of the better known pushpush game. On a given structure (grid, torus...), a robot can move in a specific set of directions,…
Domination game: effect of edge- and vertex-removal
Boštjan Brešar, Paul Dorbec, Sandi Klavžar +1
The domination game is played on a graph by two players, named Dominator and Staller. They alternatively select vertices of such that each chosen vertex enlarges the set of…